Method for manufacturing quartz crystal oscillator

ABSTRACT

In a method for manufacturing a quartz crystal oscillator, at least one of a chemical etching method, a physical etching method, and a mechanical method is utilized to form a quartz crystal tuning fork resonator having a quartz crystal tuning fork base, quartz crystal tuning fork tines connected to the quartz crystal tuning fork base, a fundamental mode of vibration, and a second overtone mode of vibration each comprised of a flexural mode of an inverse phase. An amplification circuit is provided having at least an amplifier. A feedback circuit is provided having the quartz crystal tuning fork resonator and capacitors. The amplifier of the amplification circuit and the quartz crystal tuning fork resonator and capacitors of the feedback circuit are electrically connected together.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a quartz crystal resonator, a quartzcrystal unit and a quartz crystal oscillator, and their manufacturingmethods.

2. Background Information

In general, a quartz crystal resonator is housed in a quartz crystalunit and a quartz crystal oscillator comprises the quartz crystal unit.For example, a quartz crystal oscillator with a quartz crystal unitcomprising a contour mode resonator such as a quartz crystal tuning forkresonator, which is capable of vibrating in a flexural mode, is widelyused as a time standard in consumer products, wearable time-keepingequipment and communication equipment (such as cellular phones,wristwatches and pagers). Recently, because of high frequency stability,miniaturization and the light weight nature of these products, the needfor a smaller quartz crystal unit and a smaller quartz crystaloscillator with a smaller quartz crystal tuning fork resonator, capableof vibrating in a flexural mode and having a high frequency stability, asmall series resistance and a high quality factor has arisen.

Heretofore, however, it has been impossible to obtain a quartz crystalunit and a quartz crystal oscillator because a conventional quartzcrystal tuning fork resonator, capable of vibrating in a flexural modecan not be obtained with a high frequency stability, a small seriesresistance and a high quality factor when it is miniaturized.

Moreover, nothing teaches figure of merit M of the present inventionwhich has an influence on a frequency stability for a flexural mode,quartz crystal tuning fork resonator capable of vibrating in afundamental mode and teaches a relationship of an amplification circuitand a feedback circuit which construct a quartz crystal oscillatingcircuit of the present invention, and also, nothing teaches a method ofmanufacturing a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode, a quartz crystal unit and a quartz crystaloscillator of the present invention.

Likewise, nothing teaches a method for manufacturing a quartz crystalunit comprising a contour mode resonator such as a width-extensionalmode quartz crystal resonator, a length-extensional mode quartz crystalresonator and a Lame mode quartz crystal resonator, and theirresonators, according to the present invention.

In addition, for example, there been has a big problem in theconventional quartz crystal oscillator with the conventional quartzcrystal tuning fork resonator, such that a fundamental mode vibration ofthe resonator jumps to a second overtone mode vibration by shock orvibration.

It is, therefore, a general object of the present invention to provideembodiments of a contour mode resonator such as a flexural mode, quartzcrystal tuning fork resonator, a width-extensional mode quartz crystalresonator, a length-extensional mode quartz crystal resonator and a Lamemode quartz crystal resonator, a quartz crystal unit with the contourmode resonator and a quartz crystal oscillator comprising a quartzcrystal oscillating circuit with a flexural mode, quartz crystal tuningfork resonator, capable of vibrating in a fundamental mode, and having ahigh frequency stability, a small series resistance and a high qualityfactor, and also to provide embodiments of a method for manufacturingthe contour mode resonator, the quartz crystal unit and the quartzcrystal oscillator, which overcome or at least mitigate one or more ofthe above problems.

SUMMARY OF THE INVENTION

The present invention relates to a flexural mode, quartz crystal tuningfork resonator, capable of vibrating in a fundamental mode and having anominal frequency of 32.768 kHz, a quartz crystal unit comprising acontour mode resonator such as a flexural mode, quartz crystal tuningfork resonator, a width-extensional mode quartz crystal resonator, alength-extensional mode quartz crystal resonator and a Lame mode quartzcrystal resonator, and a quartz crystal oscillator comprising a quartzcrystal oscillating circuit having an amplification circuit and afeedback circuit, and also relates to their manufacturing methods.

It is an object of the present invention to provide a flexural mode,quartz crystal tuning fork resonator capable of vibrating in afundamental mode and having a nominal frequency of 32.768 kHz.

It is an another object of the present invention to provide a quartzcrystal unit comprising a contour mode quartz crystal resonator.

It is a further object of the present invention to provide a quartzcrystal oscillator comprising a quartz crystal oscillating circuit witha flexural mode, quartz crystal tuning fork resonator, capable ofvibrating in a fundamental mode, and having a nominal frequency of32.768 kHz, a high frequency stability, a small series resistance R₁ anda high quality factor Q₁.

It is a still further object of the present invention to provide amethod for manufacturing a plurality of individual quartz crystal tuningfork resonators capable of vibrating in a flexural mode, a quartzcrystal unit comprising a contour mode quartz crystal resonator, a caseand a lid, and a quartz crystal oscillator comprising: a quartz crystaloscillating circuit comprising; an amplification circuit comprising anamplifier at least and a feedback circuit comprising a flexural mode,quartz crystal tuning fork resonator and capacitors at least.

According to one aspect of the present invention, there is provided amethod for manufacturing a plurality of individual quartz crystal tuningfork resonators each of which is capable of vibrating in a flexuralmode, and each of the individual quartz crystal tuning fork resonatorscomprising the steps of: forming integrally tuning fork tines each ofwhich has a length, a width and a thickness and the length greater thanthe width and the thickness, and a tuning fork base; providing grooves;and disposing electrodes inside the grooves and on sides of said tuningfork tines, and the grooves being provided at said tuning fork tines,and the electrodes being disposed opposite each other inside the groovesand on the sides of said tuning fork tines so that the electrodesdisposed opposite each other are of opposite electrical polarity andsaid tuning fork tines are capable of vibrating in inverse phase,wherein the individual quartz crystal tuning fork resonators areprovided in a quartz crystal wafer with resonance frequency higher than32.768 kHz, each of which is capable of vibrating in a fundamental mode,and next, metal films are formed on said tuning fork tines in the quartzcrystal wafer by a spattering method or an evaporation method so as toget the individual quartz crystal tuning fork resonators each of whichhas resonance frequency lower than 32.768 kHz, and wherein comprisingthe further steps of: adjusting the resonance frequency by removing apart or all of the metal films formed on said tuning fork tines in thequartz crystal wafer by laser trimming or a plasma etching method andinspecting the individual quartz crystal tuning fork resonators in thequartz crystal wafer, and when there is a failure resonator therein, itis removed from the quartz crystal wafer or something is marked on it orit is remembered by a computer.

According to a second aspect of the present invention, there is provideda method for manufacturing a quartz crystal unit comprising a contourmode quartz crystal resonator which is one of a width-extensional modequartz crystal resonator, a length-extensional mode quartz crystalresonator and a Lame mode quartz crystal resonator, a case and a lid,and said contour mode quartz crystal resonator comprising the step of:utilizing a particle method or a chemical etching method to form aresonator comprising; a vibrational portion; connecting portions locatedat ends of said vibrational portion; supporting portions connected tosaid vibrational portion through said connecting portions; andelectrodes disposed opposite each other on upper and lower faces of saidvibrational portion so that the electrodes disposed opposite each otherare of opposite electrical polarity, wherein a plurality of individualcontour mode quartz crystal resonators are formed in a quartz crystalwafer, each of which is capable of vibrating in a contour mode and asingle mode, and wherein each of said individual contour mode quartzcrystal resonators is mounted at a mounting portion of a case, and theresonance frequency of each resonator is adjusted by laser trimming or aplasma etching method so that a frequency deviation is within a range of−100 PPM to +100 PPM to a nominal frequency of less than 135 MHz whenthe quartz crystal unit is provided.

According to a third aspect of the present invention, there is provideda method for manufacturing a quartz crystal oscillator comprising: aquartz crystal oscillating circuit comprising; an amplification circuitcomprising an amplifier at least and a feedback circuit comprising aquartz crystal tuning fork resonator and capacitors at least, saidquartz crystal tuning fork resonator comprising the steps of: formingintegrally tuning fork tines each of which has a length, a width and athickness and the length greater than the width and the thickness, and atuning fork base; providing grooves; and disposing electrodes inside thegrooves and on sides of said tuning fork tines, and the grooves beingprovided at said tuning fork tines, and the electrodes being disposedopposite each other inside the grooves and on the sides of said tuningfork tines so that the electrodes disposed opposite each other are ofopposite electrical polarity and said tuning fork tines are capable ofvibrating in inverse phase, and said quartz crystal oscillating circuitcomprising the step of connecting electrically said quartz crystaltuning fork resonator, the amplifier and the capacitors at least,wherein said quartz crystal tuning fork resonator is capable ofvibrating in a flexural mode and said quartz crystal oscillating circuitcomprises said quartz crystal tuning fork resonator whose figure ofmerit M₁ of a fundamental mode vibration is larger than figure of meritM₂ of a second overtone mode vibration to suppress the second overtonemode vibration and to get a high frequency stability for the fundamentalmode vibration.

According to a fourth aspect of the present invention, there is provideda method for manufacturing a quartz crystal oscillator comprising: aquartz crystal oscillating circuit comprising; an amplification circuitcomprising a CMOS inverter and a feedback resistor, and a feedbackcircuit comprising a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode, resistors and capacitors, said quartzcrystal tuning fork resonator comprising the step of: utilizing achemical etching method to form a resonator comprising; tuning forktines each of which has a length, a width and a thickness and the lengthgreater than the width and the thickness, and a tuning fork base, andelectrodes disposed on obverse and reverse faces and on sides of saidtuning fork tines so that said tuning fork tines are capable ofvibrating in inverse phase, said quartz crystal tuning fork resonatorbeing formed in a quartz crystal wafer and a plurality of individualquartz crystal tuning fork resonators capable of vibrating each in afundamental mode being formed therein, each of which comprises: tuningfork tines and a tuning fork base; and electrodes disposed on obverseand reverse faces and on sides of the tuning fork tines, and hasresonance frequency higher than 32.768 kHz, wherein comprising thefurther steps of: forming metal films on the tuning fork tines of theindividual quartz crystal tuning fork resonators in the quartz crystalwafer by a spattering method or an evaporation method so as to get theindividual quartz crystal tuning fork resonators each of which hasresonance frequency of 29.4 kHz to 32.75 kHz; mounting each resonator ata mounting portion of a case; and adjusting the resonance frequency ofthe each resonator by laser trimming or a plasma etching method so thatit is within a range of 32.764 kHz to 32.772 kHz when a quartz crystalunit comprising said quartz crystal tuning fork resonator is provided,wherein said quartz crystal oscillating circuit comprising theamplification circuit and the feedback circuit is constructed so that aratio of an absolute value of negative resistance, |−RL₁| of afundamental mode vibration of the amplification circuit and seriesresistance R₁ of the fundamental mode vibration is larger than that ofan absolute value of negative resistance, |−RL₂| of a second overtonemode vibration of the amplification circuit and series resistance R₂ ofthe second overtone mode vibration, and an output signal of said quartzcrystal oscillating circuit is outputted through a buffer circuit andhas a frequency of 32.764 kHz to 32.772 kHz, and wherein comprising thefurther step of inspecting the individual quartz crystal tuning forkresonators formed in the quartz crystal wafer, and when there is afailure resonator therein, it is removed from the quartz crystal waferor something is marked on it or it is remembered by a computer.

The present invention will be more fully understood by referring to thefollowing detailed specification and claims taken in connection with theappended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a general view of a flexural mode, quartz crystal tuningfork resonator embodying the present invention;

FIG. 2 shows a cross-sectional view of the tuning fork base along line2—2 of FIG. 1 illustrating an electrode construction;

FIG. 3 shows a plan view of a quartz crystal tuning fork resonator ofFIG. 1;

FIG. 4 shows a plan view of a flexural mode, quartz crystal tuning forkresonator embodying the present invention;

FIG. 5 a and FIG. 5 b show a plan view and a side view of a contour modequartz crystal resonator capable of vibrating in a width-extensionalmode embodying the present invention;

FIG. 6 shows a cross-sectional view of a quartz crystal unit embodyingthe present invention, and in which a quartz crystal tuning forkresonator is housed;

FIG. 7 shows a step diagram of a method for manufacturing a quartzcrystal tuning fork resonator and a quartz crystal unit of the presentinvention;

FIG. 8 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit which constructs a quartz crystal oscillator of the presentinvention;

FIG. 9 shows a diagram of the feedback circuit of FIG. 8;

FIG. 10 shows a cross-sectional view of a quartz crystal oscillatorembodying the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the drawings, the embodiments of the present inventionwill be described in more detail.

FIG. 1 shows a general view of a flexural mode, quartz crystal tuningfork resonator 10 embodying the present invention and its coordinatesystem o-xyz. A cut angle θ, which has a typical value of 0° to 10°, isrotated from a Z-plate perpendicular to the z axis about the x axis. Thequartz crystal resonator 10 comprises two tuning fork tines 20 and 26and a tuning fork base 40. The tines 20 and 26 have grooves 21 and 27respectively, with the grooves 21 and 27 extending into the base 40. Inaddition, the base 40 has the additional grooves 32 and 36.

FIG. 2 shows a cross-sectional view of the tuning fork base 30 for thequartz crystal resonator 10 along line 2—2 of FIG. 1. In FIG. 2, theshape of the electrode construction within the base 40 for the quartzcrystal resonator of FIG. 1 is described in detail. The section of thebase 40 for the quartz crystal resonator of FIG. 1 is described indetail. The section of the base 40 which couples to the tine 20 has thegrooves 21 and 22 cut into the obverse and reverse faces of the base 40.Also, the section of the base 40 which couples to the tine 26 has thegrooves 27 and 28 cut into the obverse and reverse faces of the base 40.In addition to these grooves, the base 40 has the grooves 32 and 36 cutbetween the grooves 21 and 27, and also, the base 40 has the grooves 33and 37 cut between the grooves 22 and 28.

Furthermore, the grooves 21 and 22 have the first electrodes 23 and 24both of the same electrical polarity, the grooves 32 and 33 have thesecond electrodes 34 and 35 both of the same electrical polarity, thegrooves 36 and 37 have the third electrodes 38 and 39 both of the sameelectrical polarity, the grooves 27 and 28 have the fourth electrodes 29and 30 both of same electrical polarity and the sides of the base 40have the fifth and sixth electrodes 25 and 31, each of oppositeelectrical polarity. In more detail, the fifth, fourth, and secondelectrodes 25, 29, 30, 34 and 35 have the same electrical polarity,while the first, sixth and third electrodes 23, 24, 31, 38 and 39 havethe opposite electrical polarity to the others. Two electrode terminalsE—E′ are constructed. That is, the electrodes disposed inside thegrooves constructed opposite each other in the thickness (z axis)direction have the same electrical polarity. Also, the electrodesdisposed opposite each other across adjoining grooves have oppositeelectrical polarity.

In addition, the resonator has a thickness t of the tuning fork tines orthe tuning fork tines and the tuning fork base, and a groove thicknesst₁. It is needless to say that the electrodes are disposed inside thegrooves and on the sides of the tuning fork tines. In this embodiment,the first electrodes 23 and 24 are disposed at the tine and the base,and also, the fourth electrodes 29 and 30 are disposed at the tine andthe base. In addition, the electrodes are disposed on the sides of thetines opposite each other to the electrodes disposed inside the grooves.Namely, the electrodes are disposed opposite each other inside thegrooves and on the sides of the tuning fork tines so that the electrodesdisposed opposite each other are of opposite electrical polarity and thetuning fork tines are capable of vibrating in inverse phase.

Now, when a direct current (DC) voltage is applied between the electrodeterminals E—E′ (E terminal: plus, E′ terminal: minus), an electric fieldEx occurs in the arrow direction as shown in FIG. 2. As the electricfield Ex occurs perpendicular to the electrodes disposed on the base andthe tines, the electric field Ex has a very large value and a largedistortion occurs at the base and the tines, so that a flexural mode,quartz crystal tuning fork resonator is obtained with a small seriesresistance R₁ and a high quality factor Q₁, even if it is miniaturized.

FIG. 3 shows a plan view of the resonator 10 of FIG. 1. In FIG. 3, theconstruction and the dimension of grooves 21, 27, 32 and 36 aredescribed in detail. The groove 21 is constructed to include a portionof the central line 41 of the tine 20, the groove 27 is similarlyconstructed to include a portion of the central line 42 of the tine 26.The width W₂ of the grooves 21 and 27 (groove width W₂) which include aportion of the central lines 41 and 42 respectively, is preferablebecause moment of inertia of the tines 20 and 26 becomes large and thetines can vibrate in a flexural mode very easily. As a result of whichthe flexural mode, tuning fork, quartz crystal resonator capable ofvibrating in a fundamental mode can be obtained with a small seriesresistance R₁ and a high quality factor Q₁.

In more detail, when part widths W₁, W₃ and groove width W₂ are taken,the tine width W of the tines 20 and 26 has a relationship ofW=W₁+W₂+W₃, and a part or all of at least one of the grooves isconstructed so that W₁≧W₃ or W₁<W₃. In addition, the groove width W₂ isconstructed so that W₂≧W₁, W₃. In this embodiment, also, the grooves areconstructed at the tuning fork tines so that a ratio(W₂/W) of the groovewidth W₂ and the tine width W is larger than 0.35 and less than 1, and aratio(t₁/t) of the groove thickness t₁ and the thickness t of the tuningfork tines (tine thickness t) is less than 0.79, preferably, within arange of 0.01 to 0.79 to obtain very large moment of inertia of thetuning fork tines. That is to say, the flexural mode, quartz crystaltuning fork resonator, capable of vibrating in the fundamental mode, andhaving a high frequency stability can be provided with a small seriesresistance R₁, a high quality factor Q₁ and a small capacitance ratio r₁because electromechanical transformation efficiency of the resonatorbecomes large markedly.

Likewise, length l₁ of the grooves 21 and 27 of the tines 20 and 26extends into the base 40 in this embodiment (which has a dimension ofthe length l₂ and the length l₃ of the grooves). Therefore, groovelength and length of the tuning fork tines are given by (l₁-l₃) and(l-l₂), respectively, and a ratio of (l₁-l₃) and (l-l₂) is within arange of 0.4 to 0.8 to get a flexural mode, quartz crystal tuning forkresonator with series resistance R₁ of a fundamental mode vibrationsmaller than series resistance R₂ of a second overtone mode vibration

Furthermore, the total length l is determined by the frequencyrequirement and the size of the housing case. At the same time, to get aflexural mode, quartz crystal tuning fork resonator capable of vibratingeasily in a fundamental mode with suppression of the second overtonemode vibration which is unwanted mode vibration, there is a closerelationship between the groove length l₁ and the total length l.Namely, a ratio(l₁/l) of the groove length l₁ and the total length l iswithin a range of 0.2 to 0.78 because the quantity of charges whichgenerate within the grooves and on the sides of the tuning fork tines orthe tuning fork tines and the tuning fork base can be controlled by theratio, as a result, the second overtone mode vibration can be suppressedsubstantially, and simultaneously, a frequency stability of thefundamental mode vibration gets high. Therefore, the flexural mode,quartz crystal tuning fork resonator, capable of vibrating easily in thefundamental mode and having the high frequency stability can beprovided.

In more detail, series resistance R₁ of the fundamental mode vibrationbecomes smaller than series resistance R₂ of the second overtone modevibration. Namely, R₁<R₂, preferably, R₁<0.86R₂, therefore, a quartzcrystal oscillator (oscillator circuit) comprising an amplifier (CMOSinverter), capacitors, resistors(resistance elements) and a quartzcrystal unit with the quartz crystal tuning fork resonator of thisembodiment can be obtained, which is capable of vibrating in thefundamental mode very easily. In addition, in this embodiment thegrooves 21 and 27 of the tines 20 and 26 extend into the base 40 inseries, but embodiment of the present invention includes a plurality ofgrooves divided into the length direction of the tuning fork tines. Inaddition, the grooves may be constructed only at the tuning forktines(l₃=0), as will be shown in FIG. 4.

In this embodiment, the groove length l₁ corresponds to electrode lengthdisposed inside the grooves, though the electrode is not shown in FIG.3, but, when the electrode length is less than the groove length, thelength l₁ is of the electrode length. Namely, the ratio(l₁/l) in thiscase is expressed by a ratio of electrode length l₁ of the grooves andthe total length l. Also, a fork portion of this embodiment has arectangular shape, but this invention is not limited to this, forexample, the fork portion may have a U shape.

In addition, a space of between the tuning fork tines is given by W₄,and in this embodiment, the space W₄ and the groove width W₂ areconstructed so that W₄≧W₂, and more, the space W₄ is within a range of0.05 mm to 0.35 mm and the width W₂ is within a range of 0.02 mm to0.068 mm because it is easy to form a tuning fork shape and grooves ofthe tuning fork tines separately by a photo-lithographic process and anetching process, as a result, a frequency stability for a fundamentalmode vibration gets higher than that for a second overtone modevibration. In this embodiment, a quartz crystal wafer with the thicknesst of 0.05 mm to 0.12 mm is used. But, it is possible to use the waferthicker than 0.12 mm.

In more detail, to obtain a flexural mode, quartz crystal tuning forkresonator with a high frequency stability which gives high timeaccuracy, it is necessary to obtain the resonator whose resonancefrequency is not influenced by shunt capacitance because quartz crystalis a piezoelectric material and the frequency stability is verydependent on the shunt capacitance. In order to decrease the influenceon the resonance frequency by the shunt capacitance, figure of meritM_(i) plays an important role. Namely, the figure of merit M_(i) thatexpresses inductive characteristics, electromechanical transformationefficiency and a quality factor of a flexural mode, quartz crystaltuning fork resonator, is defined by a ratio (Q_(i)/r_(i)) of a qualityfactor Q_(i) and capacitance ratio r_(l,) namely, M_(i) is given byM_(i)=Q_(i)/r_(i), where i shows vibration order of a quartz crystaltuning fork resonator, and for example, when i=1 and 2, figures of meritM₁ and M₂ are for a fundamental mode vibration and a second overtonemode vibration, respectively.

Also, a frequency difference Δf of resonance frequency f_(s) ofmechanical series independent on the shunt capacitance and resonancefrequency f_(r) dependent on the shunt capacitance is inverselyproportional to the figure of merit M_(i). The larger the value M_(i)becomes, the smaller the difference Δf becomes. Namely, the influence onthe resonance frequency f_(r) by the shunt capacitance decreases becauseit is close to the resonance frequency f_(s). Accordingly, the largerthe M_(i) becomes, the higher the frequency stability of the flexuralmode, quartz crystal tuning fork resonator becomes because the resonancefrequency f_(r) of the resonator is almost never dependent on the shuntcapacitance whose value changes with time. Namely, the flexural mode,quartz crystal tuning fork resonator can be provided with a high timeaccuracy.

In detail, a quartz crystal tuning fork resonator capable of vibratingin a flexural mode can be obtained with figure of merit M₁ of afundamental mode vibration larger than figure of merit M₂ of a secondovertone mode vibration by the above-described tuning fork shape,grooves and dimensions. That is to say, M₁>M₂. As an example, whenresonance frequency of a quartz crystal tuning fork resonator is about32.768 kHz for a fundamental mode vibration and the resonator has avalue of W₂/W=0.5, t₁/t=0.34 and l₁/l=0.48, though there is adistribution in production, the quartz crystal tuning fork resonator hasa value of M₁>65 and M₂<30, respectively.

Namely, the flexural mode, quartz crystal tuning fork resonator which iscapable of vibrating in the fundamental mode can be provided with highinductive characteristics, good electromechanical transformationefficiency (small capacitance ratio r₁ and small series resistance R₁)and a high quality factor. As a result, a frequency stability of thefundamental mode vibration becomes higher than that of the secondovertone mode vibration, and simultaneously, the second overtone modevibration can be suppressed because capacitance ratio r₂ and seriesresistance R₂ of the second overtone mode vibration become larger thancapacitance ratio r₁ and series resistance R₁ of the fundamental modevibration, respectively.

Therefore, the resonator capable of vibrating in the fundamental modevibration can be provided with a high time accuracy because it has thehigh frequency stability. Consequently, a quartz crystal oscillatingcircuit comprising the flexural mode, quartz crystal tuning forkresonator of this embodiment outputs a frequency of the fundamental modevibration as an output signal, and the frequency of the output signalhas a very high stability, namely, an excellent time accuracy. In otherwords, the quartz crystal oscillator of this embodiment has a remarkableeffect such that a frequency change by ageing becomes very small. Also,a frequency of a fundamental mode vibration of the present invention isless than 200 kHz, preferably, within a range of 10 kHz to 200 kHz.Especially, 32.768 kHz is used widely.

In addition, groove length l₁ of the present invention is length ofgrooves constructed at tuning fork tines so that the ratio(t₁/t) of thegroove thickness t₁ and the tine thickness t is less than 0.79, and theratio(W₂/W) of the groove width W₂ and the tine width W is larger than0.35 and less than 1, when the grooves are constructed only at thetuning fork tines, and also, when the grooves constructed at the tuningfork tines extend into a tuning fork base and at least one groove isconstructed between the grooves extended into the tuning fork base,groove length l₁ of the present invention is length of groovesconstructed at the tuning fork tines and the tuning fork base(groovelength l₃).

Namely, when the grooves constructed at the tuning fork tines extendinto the tuning fork base and at least one groove is not constructedbetween the grooves extended into the tuning fork base, the groovelength l₁ of the present invention is length of grooves constructed atthe tuning fork tines. Also, when the grooves of the tines are dividedinto the length direction thereof or connected via at least one stepportion, the groove length l₁ is total length of the length directionsatisfying the ratios(t₁/t) and (W₂/W) described above. In addition, thegroove thickness t₁ of the present invention is the thinnest thicknessof the grooves because quartz crystal is an anisotropic material and thegroove thickness t₁ has a distribution when it is formed by a chemicaletching method.

FIG. 4 shows a plan view of a flexural mode, quartz crystal tuning forkresonator 45 embodying the present invention. The resonator 45 comprisestuning fork tines 46, 47 and a tuning fork base 48. The tines 46, 47 andthe base 48 are formed integrally by a chemical etching process. In thisembodiment, the base 48 has cut portions 53 and 54. Also, a groove 49 isconstructed to include a portion of the central line 51 of the tine 46,a groove 50 is similarly constructed to include a portion of the centralline 52 of the tine 47. In this embodiment, the grooves 49 and 50 areconstructed at a part of the tines 46 and 47, and have groove width W₂and groove length l₁.

In this embodiment, though electrodes are not shown in FIG. 4, theelectrodes are disposed inside the grooves 49, 50 and on sides of thetuning fork tines 46 and 47, similar to FIG. 2. In detail, theelectrodes are disposed opposite each other inside the grooves and onthe sides of the tuning fork tines so that the electrodes disposedopposite each other are of opposite electrical polarity and the tuningfork tines are capable of vibrating in inverse phase.

Also, in this embodiment, the width W₂ of the grooves 49 and 50 (groovewidth W₂) which include a portion of the central lines 51 and 52,respectively, is preferable because moment of inertia of the tines 46and 47 becomes large and the tines are capable of vibrating in aflexural mode very easily. Also, though grooves of reverse face of thetines are not shown in FIG. 4, the grooves are constructed opposite eachother to the grooves 49 and 50 at the reverse face of the tines 46 and47, and electrodes are disposed inside the grooves and on sides of thetines, similar to FIG. 2.

In addition, the base 48 has cut portions 53 and 54, and the cut base 48has a dimension of width W₅ (tines side) and width W₆ (opposite side tothe tines side). When the base 48 is mounted at a mounting portion of acase of surface mounting type or tubular type by solder or conductiveadhesives, it is necessary to satisfy W₆≧W₅ to decrease energy losses byvibration. The cut portions 53 and 54 are very effective to decrease theenergy losses. Therefore, the flexural mode, quartz crystal tuning forkresonator, capable of vibrating in the fundamental mode and having thehigh frequency stability (high time accuracy) can be provided with asmall series resistance R₁ and a high quality factor Q₁. Also, the widthdimensions W=W₁+W₂+W₃ and W₄, and the length dimensions l₁, l₂ and l areas already described in relation to FIG. 3.

FIG. 5 a and FIG. 5 b are a plan view and a side view of a contour modequartz crystal resonator capable of vibrating in a width-extensionalmode embodying the present invention, so called a width-extensional modequartz crystal resonator 62. The resonator 62 comprises vibrationalportion 63, connecting portions 66, 69 and supporting portions 67, 80including respective mounting portions 68, 81. In addition, thesupporting portions 67 and 80 have respective-holes 67 a and 80 a. Also,electrodes 64 and 65 are disposed opposite each other on upper and lowerfaces of the vibrational portion 63, the electrodes have oppositeelectrical polarities. Namely, a pair of electrodes is disposed on thevibrational portion. In this case, a fundamental mode vibration can beexcited easily.

In addition, the electrode 64 extends to the mounting portion 81 throughthe one connecting portion 69 and the electrode 65 extends to themounting portion 68 through the other connecting portion 66. In thisembodiment, the electrodes 64 and 65 disposed on the vibrational portion63 extend to the mounting portions of the different direction eachother. However, a resonator with the same characteristics as saidresonator can be obtained, even if the electrodes 64 and 65 extend tothe mounting portions of the same direction each other. The resonator inthis embodiment is mounted on fixing portions of a case or a lid at themounting portions 68 and 81 by conductive adhesives or solder.

With respect to a cutting angle of the width-extensional mode quartzcrystal resonator, it is shown here. First, a quartz crystal plateperpendicular to x axis, so called, X plate quartz crystal is taken.Width W₀, length L₀ and thickness T₀ which are each dimension of the Xplate quartz crystal correspond to the respective directions of y , zand x axes.

Next, this X plate quartz crystal is, first, rotated with an angle θ_(x)of −25° to +25° about the x axis, and second, rotated with an angleθ_(y) of −30° to +30° about y′ axis which is the new axis of the y axis.In this case, the new axis of the x axis changes to x′ axis and the newaxis of the z axis changes to z″ axis because the z axis is rotatedtwice about two axes. the width-extensional mode quartz crystalresonator of the present invention is formed from the quartz crystalplate with the rotation angles.

In other words, according to an expression of IEEE notation, a cuttingangle of the width-extensional mode quartz crystal resonator of thepresent invention can be expressed by XZtw(−25°-+25°)/(−30°-+30°). Also,when a turn over temperature point T_(p) is taken in a vicinity of roomtemperature, a cutting angle of the quartz crystal resonator may bewithin a range of XZt(−12°-−13.5°) or XZt(−18.5°-−19.8°) orXZtw(−13°-−18°)/±(+0.5°-+30°). Namely, said three kinds of cuttingangles in this embodiment is in the same direction as the cutting angleof the DT cut quartz crystal resonator, which is formed from a rotatedY-plate about the x axis whose Y-plate is perpendicular to the y axis.

Moreover, the vibrational portion 63 has a dimension of width W₀, lengthL₀ and thickness Z₀, also, width W₀, length L₀ and thickness T₀correspond to y′, z″ and x′ axes, respectively. That is, the electrodes64 and 65 are disposed on the upper and lower faces of the vibrationalportion 63 perpendicular to the x′ axis.

In addition, the vibrational portion 63 has a dimension of length L₀greater than width W₀ and thickness T₀ smaller than the width W₀.Namely, a coupling between a width-extensional mode and alength-extensional mode gets so small as it can be ignored, as a resultof which, the quartz crystal resonator can vibrate in a singlewidth-extensional mode, and also, a width-to-length ratio (W₀/L₀) has avalue smaller than 0.7 to provide the resonator with a small seriesresistance R₁ by increasing electrode area of the vibrational portion.In addition, a thickness-to-width ratio (T₀/W₀) has a value smaller than0.85 to provide the resonator with a small R₁ by increasing theintensity of an electric field E_(x), These actual dimensions are,therefore, determined by the requirement characteristics for thewidth-extensional mode quartz crystal resonator.

In more detail, resonance frequency of the width-extensional mode quartzcrystal resonator is inversely proportional to width W₀, and it isalmost independent on such an other dimension as length L₀, thicknessT₀, connecting portions and supporting potions. Also, in order to obtaina width-extensional mode quartz crystal resonator with a frequency of 4MHz, the width W₀ is about 0.7 mm. Thus, the miniature width-extensionalmode quartz crystal resonator can be provided with a frequency less than135 MHz, preferably, within a range of 1 MHz to 135 MHz becauseresonance frequency of the resonator is inversely proportional to thewidth W₀. Also, the resonator capable of vibrating in a singlewidth-extensional mode can be obtained from the relation of saiddimensions.

Consequently, a quartz crystal oscillator comprising a quartz crystaloscillating circuit comprising the resonator of this embodiment having ahigh electromechanical transformation efficiency can be provided with asmall series resistance R₁ and a high quality factor Q. Also, the quartzcrystal oscillating circuit comprises an amplification circuitcomprising an amplifier at least and a feedback circuit comprising thequartz crystal resonator and capacitors at least. In detail, theamplification circuit comprises a CMOS inverter and a feedback resistorand the feedback circuit comprises a drain resistor, the resonator, acapacitor of a gate side and a capacitor of a drain side. Therefore, anoutput signal of the quartz crystal oscillator of this embodiment isused as a clock signal.

Now, when an alternating current (AC) voltage is applied between theelectrodes 64 and 65 shown in FIG. 5 b, an electric field E_(x) occursalternately in the thickness direction, as shown by the arrow directionof the solid and broken lines. Consequently, the vibrational portion 63is capable of extending and contracting in the width direction. In thisembodiment, though the width-extensional mode quartz crystal resonatoris described in detail, which is one of a contour mode quartz crystalresonator, this invention is not limited to this, but includes alength-extensional mode quartz crystal resonator and a Lame mode quartzcrystal resonator, each of which is capable of vibrating in a contourmode, and has a vibrational portion, connecting portions and supportingportions respectively.

Especially, for the Lame mode quartz crystal resonator, the vibrationalportion and the supporting portions are connected at corners of thevibrational portion through the connecting portions and electrodes aredisposed opposite each other on upper and lower faces of the vibrationalportion so that the electrodes opposite each other are of oppositeelectrical polarity. Also, the length-extensional mode quartz crystalresonator of the present invention can be obtained by replacing thewidth with the length and the length with the width of thewidth-extensional mode quartz crystal resonator. Therefore, theconnecting portions and the supporting portions are constructed in thewidth direction and the connecting portions are connected at ends of thevibrational portion.

FIG. 6 shows a cross-sectional view of a quartz crystal unit embodyingthe present invention. In this embodiment, the quartz crystal unit 170comprises a flexural mode, quartz crystal tuning fork resonator 70, acase 71 and a lid 72. In more detail, the resonator 70 is mounted at amounting portion 74 of the case 71 by conductive adhesives 76 or solder.Also, the case 71 and the lid 72 are connected through a connectingmember 73. The resonator 70 in this embodiment is the same resonator asone of the flexural mode, quartz crystal tuning fork resonators 10 and45 described in detail in FIG. 1-FIG. 4. Also, in this embodiment,circuit elements are connected at outside of the quartz crystal unit toget a quartz crystal oscillator. Namely, only the quartz crystal tuningfork resonator is housed in the unit (package) and also, it is housed inthe unit in vacuum. In this embodiment, the quartz crystal unit ofsurface mounting type is shown, but the quartz crystal tuning forkresonator may be housed in a unit of tubular type. For example, when aquartz crystal tuning fork resonator is housed in the unit of tubulartype, a case has two lead wires as a mounting portion and the resonatoris mounted on the two lead wires. This is called a quartz crystal unitof tubular type.

In this embodiment, the quartz crystal unit comprises the flexural mode,quartz crystal tuning fork resonator, but may comprise thelength-extensional mode quartz crystal resonator or the Lame mode quartzcrystal resonator described above in detail, instead of the tuning forkresonator.

In addition, a member of the case and the lid is ceramics or glass and ametal or glass, respectively, and a connecting member is a metal orglass with low melting point. Also, a relationship of the resonator, thecase and the lid described in this embodiment is applied to a quartzcrystal oscillator of the present invention which will be described inFIG. 10

Next, a method for manufacturing a quartz crystal resonator, a quartzcrystal unit and a quartz crystal oscillator of the present invention isdescribed in detail, according to the manufacturing steps.

FIG. 7 shows an embodiment of a method for manufacturing a quartzcrystal resonator, a quartz crystal unit and a quartz crystal oscillatorof the present invention and a step diagram embodying the presentinvention. In this embodiment, a quartz crystal tuning fork resonatorcapable of vibrating in a flexural mode is described. The signs of S-1to S-12 are the step numbers. First, S-1 shows a cross-sectional view ofa quartz crystal wafer 140. Next, in S-2 metal film 141, for example,chromium and gold on the chromium are, respectively, disposed on upperand lower faces of the quartz crystal wafer 140 by an evaporation methodor a spattering method. In addition, resist 142 is spread on said metalfilm 141 in S-3, and after the metal film 141 and the resist 142 wereremoved except those of tuning fork shape by a photo-lithographicprocess and an etching process, the tuning fork shape having tuning forktines 143, 144 and a tuning fork base 145, as be shown in S-4, isintegrally formed by a chemical etching process. In S-4, the resist andthe metal film disposed on the tuning fork shape are removed after itwas formed. When the tuning fork shape is formed, cut portions may beformed at the tuning fork base. In FIG. 7 the formation of a piece oftuning fork shape is shown, but, a plurality of individual tuning forkshapes are actually formed in a quartz crystal wafer.

Similar to the steps of S-2 and S-3, metal film and resist are spreadagain on the tuning fork shape of S-4 and grooves 146, 147, 148 and 149each of which has two step difference portions along the lengthdirection of the tuning fork tines, are formed at the tuning fork tines143, 144 by a photo-lithographic process and an etching process, and theshape of S-5 is obtained after all of the resist and the metal film wereremoved. In addition, metal film and resist are spread again on theshape of S-5 and electrodes which are of opposite electrical polarity,are disposed opposite each other on sides of the tuning fork tines andinside the grooves thereof, as be shown in S-6.

Namely, electrodes 150, 153 disposed on the sides of the tuning forktine 143 and electrodes 155, 156 disposed inside the grooves 148, 149 ofthe tuning fork tine 144 have the same electrical polarity. Similarly,electrodes 151, 152 disposed inside the grooves 146, 147 of the tuningfork tine 143 and electrodes 154, 157 disposed on the sides of thetuning fork tine 144 have the same electrical polarity. Two electrodeterminals are, therefore, constructed. In more detail, when analternating current (AC) voltage is applied between the terminals, thetuning fork tines are capable of vibrating in a flexural mode of inversephase because said electrodes disposed on step difference portions ofthe grooves and the electrodes disposed opposite to the said electrodeshave opposite electrical polarity. In the step of S-6, a piece offlexural mode, quartz crystal tuning fork resonator capable of vibratingin a fundamental mode is shown in the quartz crystal wafer, but aplurality of individual quartz crystal tuning fork resonators, each ofwhich comprises tuning fork tines and a tuning fork base capable ofvibrating in a flexural mode and has resonance frequency higher than32.768 kHz in the fundamental mode vibration, are actually formed in thequartz crystal wafer.

Next, metal films are formed on the tuning fork tines of the individualquartz crystal tuning fork resonators in the quartz crystal wafer by aspattering method or an evaporation method so as to get the individualquartz crystal tuning fork resonators each of which has resonancefrequency lower than 32.768 kHz, preferably, within a range of 29.4 kHzto 32.75 kHz.

In addition, resonance frequency for the individual resonators isadjusted by a separate step of at least twice and the first adjustmentof resonance frequency for the individual resonators is performed in thequartz crystal wafer by laser trimming or a plasma etching method sothat the resonance frequency of the individual resonators is within arange of 32.2 kHz to 33.08 kHz. The adjustment of frequency by lasertrimming or a plasma etching method is performed by trimming the metalfilms disposed on the tuning fork tines to increase the resonancefrequency, on the other hand, the adjustment of frequency by anevaporation method is performed by adding mass such as a metal on tuningfork tines to decrease the resonance frequency. Namely, those methodscan change the resonance frequency of the resonators. Also, theindividual resonators formed in the quartz crystal wafer are inspectedtherein and when there is a failure resonator, it is removed from thequartz crystal wafer or something is marked on it or it is remembered bya computer.

In this embodiment, the tuning fork shape is formed from the step of S-3and after that, the grooves are formed at the tuning fork tines, namely,the tuning fork tines are formed before the grooves are formed, but thisinvention is not limited to said embodiment, for example, the groovesare first formed from the step of S-3 and after that, the tuning forkshape may be formed, namely, the grooves are formed before the tuningfork tines are formed. Also, the tuning fork shape and the grooves maybe formed simultaneously, namely, the tuning fork tines and the groovesare formed simultaneously. In addition, the grooves each of which hastwo step difference portions along the direction of length of the tuningfork tines, are formed in this embodiment, but, each of the grooves mayhave step difference portions more than two along the length directionof the tines, at least two of which are connected via at least one stepportion.

Also, in this embodiment, though the grooves are constructed at thetuning fork tines and the electrodes are disposed inside the grooves,this invention is not limited to this, namely, the grooves may not beconstructed at the tuning fork tines. In more detail, the tuning forktines have obverse and reverse faces and sides and electrodes aredisposed on the obverse and reverse faces and the sides of the tines. Inaddition, electrodes disposed on obverse and reverse faces of tuningfork tines of the present invention implies electrodes disposed on theobverse and reverse faces of the tuning fork tines, notwithstandingthere is a groove at the tines or not. Therefore, it is needless to saythat this invention includes at least one connecting electrode disposedon at least one face of the obverse and reverse faces of the tines toconnect two electrodes. As a result of which the tuning fork tines arecapable of vibrating in inverse phase.

There are two methods of A and B in the following step, as be shown byarrow signs. For the step of A, the tuning fork base 145 of the formedflexural mode, quartz crystal tuning fork resonator 160 is first mountedon mounting portion 159 of a case 158 by conductive adhesives 161 orsolder, as be shown in S-7. Next, the second adjustment of resonancefrequency for the resonator 160 is performed by laser 162 or anevaporation method or a plasma etching method in S-8 so that theresonance frequency is within a range of 32.764 kHz to 32.772 kHz whenthe resonator is housed in a package, namely, the quartz crystal unit isprovided. Finally, the case 158 and a lid 163 are connected via glass164 with the low melting point or a metal in S-9. In this case, theconnection of the case and the lid is performed in vacuum because thecase 158 has no hole to close it in vacuum.

In this embodiment, though the metal films are formed on the tuning forktines of the individual quartz crystal resonators formed in the quartzcrystal wafer and resonance frequency of the individual resonators isadjusted therein by removing a part or all of the metal films by lasertrimming or a plasma etching method, the present invention is notlimited to this, namely, said steps may be omitted. In more detail, eachof the individual resonators having resonance frequency higher than32.768 kHz is mounted at a mounting portion of a case and after that,the resonance frequency is adjusted by an evaporation method so that itis within a range of 32.764 kHz to 32.772 kHz when a quartz crystal unitis provided.

In addition, though it is not visible in FIG. 7, the third frequencyadjustment may be performed by laser trimming after the step of theconnection of S-9 to get a small frequency deviation when a material ofthe lid is glass. As a result of which it is possible to get theresonator with the resonance frequency of 32.766 kHz to 32.77 kHz. Likethis step, when the third frequency adjustment is performed, theresonance frequency of the resonators by the second frequency adjustmentis adjusted so that it is within a range of 32.736 kHz to 32.8 kHz.

For the step of B, the tuning fork base 145 of the formed resonator 160is first mounted on mounting portion 159 of a case 165 by conductiveadhesives 161 or solder in S-10, in addition, in S-11 the case 165 and alid 163 are connected by the same way as that of S-9, in more detail,after the resonator was mounted on the mounting portion of the case orafter the resonator was mounted at the mounting portion and the case andthe lid were connected, the second adjustment of resonance frequency isperformed so that the resonance frequency is within a range of 32.764kHz to 32.772 kHz in vacuum, but, it may be within a wider range, forexample, 32.736 kHz to 32.8 kHz when the third frequency adjustment aswill be shown as follows, is performed. Finally, a hole 167 constructedat the case 165 is closed in vacuum using such a metal 166 as solder orglass with the low melting point in S-12.

Also, similar to the step of A, the third adjustment of resonancefrequency may be performed by laser trimming after the step of S-12 toget a small frequency deviation. As a result of which it is possible toget the resonator with the resonance frequency of 32.766 kHz to 32.77kHz. Thus, the resonance frequency of the resonators in the case of Aand B is finally within a range of 32.764 kHz to 32.772 kHz at most.Also, the second frequency adjustment may be performed after the caseand the lid were connected and after that, the hole is closed in vacuum.In addition, the hole is constructed at the case, but may be constructedat the lid. Also, the frequency adjustment of the present invention isperformed in vacuum or inert gas such as nitrogen gas or atmosphere, andthe values described above are values in vacuum.

Therefore, the quartz crystal tuning fork resonators each of which iscapable of vibrating in a flexural mode and the quartz crystal unitsmanufactured by the above-described method are miniaturized and realizedwith a small series resistance R₁, a high quality factor Q₁ and lowprice.

Moreover, in the above-described embodiment, though the first frequencyadjustment of the resonators is performed in the quartz crystal waferand at the same time, when there is a failure resonator, something ismarked on it or it is removed from the quartz crystal wafer, but thepresent invention is not limited to this, namely, the present inventionmay include the step to inspect the flexural mode, quartz crystal tuningfork resonators formed in the quartz crystal wafer therein, in otherwords, the step to inspect whether there is a failure resonator or notin the quartz crystal wafer. When there is the failure resonator in thewafer, it is removed from the wafer or something is marked on it or itis remembered by a computer. By including the step, it can increase amanufacturing yield of the quartz crystal resonators because it ispossible to find out the failure resonator in an early step and thefailure resonator does not go to the next step. As a result of which lowpriced flexural mode, quartz crystal tuning fork resonators can beprovided with excellent electrical characteristics. In this embodiment,the frequency adjustment is performed three times by a separate step,but may be performed at least twice by a separate step. For example, thethird frequency adjustment may be omitted.

In this embodiment, the frequency adjustment is performed by a separatestep of at least twice. However, when a plurality of individual quartzcrystal tuning fork resonators, each of which has a resonance frequencyhigher than 32.768 kHz, are formed in a quartz crystal wafer and eachresonator is mounted at a mounting portion of a case or a lid, resonancefrequency is adjusted by an evaporation method of at least once so thatit is within a range of 32.764 kHz to 32.772 kHz when a quartz crystalunit is provided.

Also, for the manufacturing method of this embodiment, the steps offorming a plurality of individual quartz crystal tuning fork resonatorhaving resonance frequency higher than 32.768 kHz by a chemical etchingmethod and changing the resonance frequency by forming metal films ontuning fork tines of the individual resonators are not included in thefrequency adjustment of the present invention.

In addition, in order to construct a quartz crystal oscillator having aquartz crystal oscillating circuit comprised of an amplification circuithaving at least an amplifier and a feedback circuit having at leastcapacitors and a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode, two electrode terminals of the resonatorsare connected electrically to the amplifier and the capacitors. Namely,the quartz crystal oscillating circuit comprises the step of connectingelectrically at least the quartz crystal tuning fork resonator, theamplifier and the capacitors. More specifically, the quartz crystaloscillating circuit is constructed and connected electrically so thatthe amplification circuit comprises a CMOS inverter and a feedbackresistor and the feedback circuit comprises the flexural mode, quartzcrystal tuning fork resonator, the drain resistor, the capacitor of agate side and the capacitor of a drain side. Also, the third frequencyadjustment may be performed after the quartz crystal oscillating circuithas been constructed.

Next, an embodiment of a method for manufacturing a quartz crystal unitcomprising a contour mode quartz crystal resonator such as awidth-extensional mode quartz crystal resonator, a length-extensionalmode quartz crystal resonator and a Lame mode quartz crystal resonator,a case and a lid is described in detail, the contour mode quartz crystalresonator comprises the step of: utilizing a particle method or achemical etching method to form a resonator comprising; avibrational-portion; connecting portions located at ends of saidvibrational portion; supporting portions connected to the vibrationalportion through the connecting portions; and electrodes disposedopposite each other on upper and lower faces of the vibrational portionso that the electrodes disposed opposite each other are of oppositeelectrical polarity.

In addition, a plurality of individual quartz crystal resonators each ofwhich is capable of vibrating in a contour mode and a single mode, areformed in a quartz crystal wafer with resonance frequency higher than anominal frequency, and metal films are formed on the vibrational portionin the quartz crystal wafer by a spattering method or an evaporationmethod so as to get the individual quartz crystal resonators each ofwhich has resonance frequency lower than the nominal frequency.

Moreover, each of the individual quartz crystal resonators is housed ina case, and the resonance frequency of each resonator is adjusted byremoving a part or all of the metal films formed on the vibrationalportion by laser trimming or a plasma etching method so that a frequencydeviation is within a range of −100 PPM to +100 PPM to the nominalfrequency. Namely, the resonator is housed in a package with thefrequency deviation.

In this embodiment, the metal films are formed on the vibrationalportion, but they may not be formed on the vibrational portion. In thiscase, a plurality of individual contour mode quartz crystal resonatorseach of which is capable of vibrating in a contour mode and a singlemode, are formed in a quartz crystal wafer with resonance frequencylower than a nominal frequency, and each of the individual quartzcrystal resonators is housed in a case, and the resonance frequency ofeach resonator is adjusted by removing a part of the electrodes formedon the vibrational portion by laser trimming or a plasma etching -methodso that a frequency deviation is within a range of −100 PPM to +100 PPMto the nominal frequency. Namely, the resonator is housed in a packagewith the frequency deviation.

As described above, the contour mode quartz crystal resonators in theembodiment have such complicated shapes as comprise the vibrationalportion, the connecting portions and the supporting portions. Also, theresonators in this embodiment of the present invention are generallyprocessed by a chemical etching method, but, when the etching speedwhich is very dependent on a cutting angle is extremely slow, it is verydifficult and impossible to process the resonators by the chemicaletching method. In this case, the resonators in this embodiment of thepresent invention are, therefore, processed by a physical method or amechanical method, and the resonators are formed integrally by at leastone method.

Namely, particles with mass are collided with a quartz crystal platecovered by a resist corresponding to the shape of resonators by aphysical or mechanical method, as a result of which the shapes of theresonators are processed because atoms or molecules of the quartzcrystal plate scatter. This method is called a “particle method”. Thismethod is substantially different from the chemical etching method andhas a feature that the processing speed is also very fast.

According to the particle method, low priced quartz crystal resonatorscan be provided similar to the chemical etching method because theprocessing time of outward shapes for the resonators shorten extremely.For this particle method, a resist with elastic characteristics is usedto prevent the resist form defacement by particles. As the resist, forexample, a plastic resist for use in blast processing is well known.Also, for this particle method, for example, it is preferable to useparticles of GC#1000 to GC#6000 or ion atoms or ion molecules as theparticles for use in processing. Especially, a method by ion etching iscalled “plasma etching method” in the present invention.

Additionally, an insulation material such as S_(i)O₂ may be constructedon obverse and reverse faces of the width W₁ and the width W₃ of thetuning fork tines to prevent a short circuit of between the electrodesof the sides and the grooves thereof, and the insulation material isformed by a spattering method or an evaporation method. Also, when atuning fork shape comprising tuning fork tines and a tuning fork base isformed by a photo-lithographic process and an etching process, cutportions may be also formed simultaneously at the tuning fork base.

Likewise, in the present embodiments the flexural mode quartz crystalresonator of tuning fork type has two tuning fork tines, but embodimentsof the present invention include tuning fork tines more than two. Inaddition, the quartz crystal tuning fork resonators of the presentembodiments are housed in a package (unit) of surface mounting typecomprising a case and a lid, but may be housed in a package of tubulartype.

FIG. 8 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit constructing a quartz crystal oscillator of the presentinvention. In this embodiment, the quartz crystal oscillating circuit 1comprises an amplifier (CMOS Inverter) 2, a feedback resistor 4, drainresistor 7, capacitors 5, 6 and a flexural mode, quartz crystal tuningfork resonator 3. Namely, the quartz crystal oscillating circuit 1comprises an amplification circuit 8 having the amplifier 2 and thefeedback resistor 4, and a feedback circuit 9 having the drain resistor7, the capacitors 5, 6 and the flexural mode quartz crystal resonator 3.In addition, an output signal of the quartz crystal oscillating circuit1 comprising the flexural mode, quartz crystal tuning fork resonator 3,capable of vibrating in a fundamental mode, is outputted through abuffer circuit (not shown in FIG. 8) from a drain side of the amplifier(CMOS Inverter).

In detail, a frequency of the fundamental mode vibration is outputtedthrough a buffer circuit as an output signal. According to the presentinvention, a nominal frequency of the fundamental mode vibration is32.768 kHz. Also, the present invention includes a divided frequency ofthe output signal having the frequency of 32.764 kHz to 32.772 kHz by adivided circuit. In more detail, the quartz crystal oscillator in thisembodiment comprises the quartz crystal oscillating circuit and thebuffer circuit, in other words, the quartz crystal oscillating circuitcomprises the amplification circuit and the feedback circuit, and theamplification circuit comprises the amplifier at least and the feedbackcircuit comprises the flexural mode, quartz crystal tuning forkresonator and the capacitors at least. Also, the quartz crystal tuningfork resonators each of which is capable of vibrating in a flexural modehave been already described in FIG. 1-FIG. 4 in detail.

FIG. 9 shows a diagram of the feedback circuit of FIG. 8. Now, whenangular frequency ω_(i) of the flexural mode, quartz crystal tuning forkresonator 3, capable of vibrating in a flexural mode, a resistance R_(d)of the drain resistor 7, capacitance C_(g), C_(d) of the capacitors 5,6, crystal impedance R_(ei) of the quartz crystal resonator 3, an inputvoltage V₁, and an output voltage V₂ are taken, a feedback rate β_(i) isdefined by β_(i)=|V₂|_(i)/|V₁|_(i), where i shows vibration order, forexample, when i=1 and 2, they are for fundamental mode vibration andsecond overtone mode vibration, namely, when i=n, it is for n^(th)overtone mode vibration.

In addition, load capacitance C_(L) is given by C_(L)=C_(g)C_(d)/(C_(g)+C_(d)), and when C_(g)=C_(d)=C_(gd) and Rd>>R_(ei), thefeedback rate β_(i) is given by β_(i)=1/(1+kC_(L) ²), where k isexpressed by a function of ω_(i), R_(d) and R_(ei). Also, R_(ei) isapproximately equal to series resistance R_(i).

Thus, it is easily understood from a relationship of the feedback rateβ_(i) and load capacitance C_(L) that the feedback rate of resonancefrequency for a fundamental mode vibration and an overtone modevibration becomes large, respectively, according to decrease of loadcapacitance C_(L). Therefore, when CL has a small value, an oscillationof the overtone mode occurs very easily, instead of that of thefundamental mode. This is the reason why a maximum amplitude of theovertone mode vibration becomes smaller than that of the fundamentalmode vibration, and the oscillation of the overtone mode satisfies anamplitude condition and a phase condition simultaneously which are thecontinuous condition of an oscillation in an oscillating circuit.

In addition, in order to suppress a second overtone mode vibration andto obtain a quartz crystal oscillator comprising a quartz crystaloscillating circuit, comprising a flexural mode, quartz crystal tuningfork resonator and having an output signal of a frequency of afundamental mode vibration, the quartz crystal oscillating circuit inthis embodiment is constructed so that it satisfies a relationship ofα₁/α₂>β₂/β₁ and α₁β₁>1, where α₁ and α₂ are a amplification rate of thefundamental mode vibration and the second overtone mode vibration of anamplification circuit, and β₁ and β₂ are a feedback rate of thefundamental mode vibration and the second overtone mode vibration of afeedback circuit.

In other words, the quartz crystal oscillating circuit is constructed sothat a ratio of the amplification rate α₁ of the fundamental modevibration and the amplification rate α₂ of the second overtone modevibration of the amplification circuit is larger than that of thefeedback rate β₂ of the second overtone mode vibration and the feedbackrate β₁ of the fundamental mode vibration of the feedback circuit, and aproduct of the amplification rate α₁ and the feedback rate β₁ of thefundamental mode vibration is larger than 1. By constructing theoscillating circuit like this, it can be provided with reduced electriccurrent consumption and the output signal of the frequency of thefundamental mode vibration.

Also, characteristics of the amplifier of the amplification circuitconstructing the quartz crystal oscillating circuit of this embodimentcan be expressed by negative resistance −RL_(i). For example, when i=1,negative resistance −RL₁ is for a fundamental mode vibration and wheni=2, negative resistance −RL₂ is for a second overtone mode vibration.In this embodiment, the quartz crystal oscillating circuit isconstructed so that a ratio of an absolute value of negative resistance,|−RL₁| of the fundamental mode vibration of the amplification circuitand series resistance R₁ of the fundamental mode vibration is largerthan that of an absolute value of negative resistance, |−RL₂| of thesecond overtone mode vibration of the amplification circuit and seriesresistance R₂ of the second overtone mode vibration. That is to say, theoscillating circuit is constructed so that it satisfies a relationshipof |−RL₁|/R₁>|−RL₂|/R₂. By constructing the oscillating circuit likethis, an oscillation of the second overtone mode can be suppressed, as aresult of which an output signal of a frequency of the fundamental modevibration can be provided because an oscillation of the fundamental modegenerates easily in the oscillating circuit.

FIG. 10 shows a cross-sectional view of a quartz crystal oscillatorembodying the present invention. The quartz crystal oscillator 190comprises a quartz crystal oscillating circuit, a case 91 and a lid 92.In this embodiment, circuit elements constructing the oscillatingcircuit are housed in a quartz crystal unit comprising a flexural mode,quartz crystal tuning fork resonator 90, the case 91 and the lid 92.Also, the quartz crystal oscillating circuit of this embodimentcomprises an amplifier 98 including a feedback resistor, the quartzcrystal tuning fork resonator 90, capacitors (not shown here) and adrain resistor (not shown here), and a CMOS inverter is used as theamplifier 98.

In addition, in this embodiment, the resonator 90 is mounted at amounting portion 94 of the case 91 by conductive adhesives 96 or solder.As described above, the amplifier 98 is housed in the quartz crystalunit and mounted at the case 91. Also, the case 91 and the lid 92 areconnected through a connecting member 93. The resonator 90 of thisembodiment is the same as one of the flexural mode, quartz crystaltuning fork resonators 10 and 45 described in detail in FIG. 1-FIG. 4.In this embodiment, though the resonator and the amplifier are housed inthe same room, the present invention is not limited to this, forexample, a room of the case is divided into two rooms by a dividedportion, and the amplifier is housed in one of the two rooms and theflexural mode, quartz crystal tuning fork resonator is housed in otherroom. Namely, the resonator and the amplifier are housed in a separateroom. Therefore, the quartz crystal oscillator of the present inventionalso includes that construction.

Likewise, in this embodiment, a piece of flexural mode, quartz crystaltuning fork resonator is housed in the unit, but the present inventionalso includes a quartz crystal unit having a plurality of individualflexural mode, quartz crystal tuning fork resonators, and at least twoof the plurality of individual resonators are connected electrically inparallel. In detail, the at least two resonators may be an individualresonator or may be an individual resonator that is formed integrally ateach tuning base through a connecting portion.

The above-described resonators are formed by at least one method ofchemical, mechanical and physical etching methods. For example, thephysical etching method is a method by ion etching, so called “plasmaetching”.

In addition, for the flexural mode quartz crystal tuning fork resonatorsof the embodiments of the present invention, the resonators are providedso that a capacitance ratio r₁ of a fundamental mode vibration getssmaller than a capacitance ratio r₂ of a second overtone mode vibration,in order to obtain a frequency change of the fundamental mode vibrationlarger than that of the second overtone mode vibration, versus the samechange of a value of load capacitance C_(L). Namely, a variable range ofa frequency of the fundamental mode vibration gets wider than that ofthe second overtone mode vibration. Also, C_(L) has a value less than 18pF to decrease electric current consumption in a quartz crystaloscillating circuit.

Moreover, capacitance ratios r₁ and r₂ of a flexural mode, quartzcrystal tuning fork resonator are given by r₁=C₀/C₁ and r₂=C₀/C₂,respectively, where C₀ is shunt capacitance in an electrical equivalentcircuit of the resonator, and C₁ and C₂ are, respectively, motionalcapacitance of a fundamental mode vibration and a second overtone modevibration in the electrical equivalent circuit of the resonator. Inaddition, the flexural mode, quartz crystal tuning fork resonator has aquality factor Q₁ for the fundamental mode vibration and a qualityfactor Q₂ for the second overtone mode vibration.

In detail, the tuning fork resonator of this embodiment is provided sothat the influence on resonance frequency of the fundamental modevibration by the shunt capacitance becomes smaller than that of thesecond overtone mode vibration by the shunt capacitance, namely, so thatit satisfies a relationship of r₁/2Q₁ ²<r₂/2Q₂ ². As a result, thetuning fork resonator, capable of vibrating in the fundamental mode andhaving a high frequency stability can be provided because the influenceon the resonance frequency of the fundamental mode vibration by theshunt capacitance becomes so extremely small as it can be ignored. Also,the present invention replaces r₁/2Q₁ ² with S₁ and r₂/2Q₂ ² with S₂,respectively, and here, S₁ and S₂ are called “stable factor offrequency” of the fundamental mode vibration and the second overtonemode vibration. Namely, S₁ and S₂ are given by S₁=r₁/2Q₁ ² and S₂=r₂/2Q₂², respectively.

In addition, when a power source is applied to the quartz crystaloscillating circuit, at least one oscillation which satisfies anamplitude condition and a phase condition of vibration starts in thecircuit, and a spent time to get to about ninety percent of the steadyamplitude of the vibration is called “rise time” here. Namely, theshorter the rise time becomes, the easier the oscillation becomes. Whenrise time t_(r1) of the fundamental mode vibration and rise time t_(r2)of the second overtone mode vibration in the circuit are taken, t_(r1)and t_(r2) are given by t_(r1)=kQ₁/(ω₁(−1+|−RL₁|/R₁)) andt_(r2)=kQ₂/(ω₂(−1+|−RL₂|/R₂)), respectively, where k is constant and ω₁and ω₂ are an angular frequency for the fundamental mode vibration andthe second overtone mode vibration, respectively.

From the above-described relation, it is possible to obtain the risetime t_(r1) of the fundamental mode vibration less than the rise timet_(r2) of the second overtone mode vibration. As an example, whenresonance frequency of a flexural mode, quartz crystal tuning forkresonator is about 32.768 kHz for a fundamental mode vibration and theresonator has a value of W₂/W=0.5, t₁/t=0.34 and l₁/l=0.48, though thereis a distribution in production, as an example, the resonator has avalue of Q₁=62,000 and Q₂=192,000, respectively. In this embodiment, Q₂has a value of about three times of Q₁. Accordingly, to obtain thet_(r1) less than the t_(r2), it is necessary to satisfy a relationshipof |−RL₁|/R₁>2|−RL₂|/R₂−1 by using a relation of ω₂=6ω₁ approximately.

Also, according to this invention, the relationship is not limited tothe quartz crystal oscillating circuit comprising the resonator in thisembodiment, but this invention includes all quartz crystal oscillatingcircuits to satisfy the relationship. By constructing the oscillatingcircuit like this, a quartz crystal oscillator with the flexural mode,quartz crystal tuning fork resonator can be provided with a short risetime. In other words, an output signal of the oscillator has a frequencyof a fundamental mode vibration of the resonator whose frequency iswithin a range of 32.764 kHz to 32.772 kHz, and is outputted through abuffer circuit. Namely, the second overtone mode vibration can besuppressed in the oscillating circuit. In this embodiment, the resonatorhas also a value of r₁=320 and r₂=10,600 as an example.

In addition, the contour mode quartz crystal resonators described in theembodiments of the present invention, each of which is a flexural mode,quartz crystal tuning fork resonator, a width-extensional mode quartzcrystal resonator, a length-extensional mode quartz crystal resonatorand a Lame mode quartz crystal resonator, can be applied to anelectronic apparatus comprising a display portion and a quartz crystaloscillator at least such as cellar phone, telephone, TV set, camera,video set, video camera, pagers, personal computer, printer, CD player,MD player, electronic musical instrument, car navigator, carelectronics, timepiece, IC card and so forth.

In detail, the contour mode quartz crystal resonators each of whichconstructs a quartz crystal oscillator comprising: a quartz crystaloscillating circuit comprising; an amplification circuit and a feedbackcircuit as described above, are used as a clock signal of the electronicapparatus. In more detail, an output signal of the quartz crystaloscillating circuit comprising the quartz crystal tuning fork resonatorcapable of vibrating in a flexural mode has a frequency of 32.764 kHz to32.772 kHz and is outputted through a buffer circuit, and the outputsignal is a clock signal which is used to display time at the displayportion of the electronic apparatus.

Likewise, an output signal of the quartz crystal oscillating circuitcomprising a width-extensional mode quartz crystal resonator or alength-extensional mode quartz crystal resonator or a Lame mode quartzcrystal resonator is outputted through a buffer circuit, and the outputsignal is a clock signal which is used except time display of theelectronic apparatus.

In the present embodiments, the metal films for frequency adjustment areformed on the tuning fork tines. As an example of the present invention,silver or gold is used as a material of the metal films and for example,the metal films are formed on at least two faces of obverse and reversefaces of the tuning fork tines. Preferably, the at least two faces areof the same faces.

As described above, it will be easily understood that the quartz crystalresonators, the quartz crystal units and the quartz crystal oscillatorsof the present invention may have the outstanding effects. For example,the quartz crystal oscillator comprising: the quartz crystal oscillatingcircuit comprising; the amplification circuit and the feedback circuithaving the flexural mode, quartz crystal tuning fork resonator, capableof vibrating in a fundamental mode and having the novel shapes, thenovel electrode construction and good electrical characteristics,according to the present invention may have the outstanding effects. Inaddition to this, while the present invention has been shown anddescribed with reference to preferred embodiments thereof, it will beunderstood by those skilled in the art that the changes in shape andelectrode construction can be made therein without departing from thespirit and scope of the present invention.

1. A method for manufacturing a quartz crystal oscillator, comprisingthe steps of: forming by at least one of a chemical etching method, aphysical etching method, and a mechanical method a quartz crystal tuningfork resonator having a quartz crystal tuning fork base and first andsecond quartz crystal tuning fork tines each connected to the quartzcrystal tuning fork base and having a first main surface and a secondmain surface opposite the first main surface, the quartz crystal tuningfork resonator having a fundamental mode of vibration and a secondovertone mode of vibration each comprised of a flexural mode of aninverse phase, a series resistance R₁ of the fundamental mode ofvibration, and a series resistance R² of the second overtone mode ofvibration; providing an amplification circuit having at least anamplifier, a negative resistance −RL₁ of a fundamental mode of vibrationthereof, and a negative resistance −RL₂ of a second overtone mode ofvibration thereof; providing a feedback circuit having the quartzcrystal tuning fork resonator and a plurality of capacitors; andelectrically connecting together the amplifier of the amplificationcircuit and the quartz crystal tuning fork resonator and capacitors ofthe feedback circuit; wherein a ratio of an absolute value of thenegative resistance −RL₁ of the fundamental mode of vibration of theamplification circuit and the series resistance R₁ of the fundamentalmode of vibration of the quartz crystal tuning fork resonator is greaterthan that of an absolute value of the negative resistance −RL₂ of thesecond overtone mode of vibration of the amplification circuit and theseries resistance R₂ of the second overtone mode of vibration of thequartz crystal tuning fork resonator; and wherein a merit value M₁ ofthe fundamental mode of vibration of the quartz crystal tuning forkresonator is greater than a merit value M₂ of the second overtone modeof vibration thereof so that the second overtone mode of vibration ofthe quartz crystal tuning fork resonator is suppressed and a highfrequency stability is obtained for the fundamental mode of vibration ofthe quartz crystal tuning fork resonator, the merit values M₁ and M₂being defined by the ratios Q_(1/r) ₁ and Q₂/r₂, respectively, where Q₁and Q₂ represent a quality factor of the fundamental mode of vibrationand the second overtone mode of vibration, respectively, of the quartzcrystal tuning fork resonator and r₁ and r₂ represent a capacitanceratio of the fundamental mode of vibration and the second overtone modeof vibration, respectively, of the quartz crystal tuning fork resonator.2. A method according to claim 1; wherein the amplification circuit hasa CMOS inverter and the feedback circuit has the capacitors and a drainresistor; and wherein the electrically connecting step comprises thestep of electrically connecting the quartz crystal tuning fork resonatorto the CMOS inverter of the amplification circuit and to the capacitorsand the drain resistor of the feedback circuit.
 3. A method according toclaim 2; wherein the forming step includes the step of forming thequartz crystal tuning fork resonator so that the quartz crystal tuningfork resonator has a frequency of 32.768 kHz; and further comprising thesteps of providing a case having an open end, providing a lid forcovering the open end of the case, disposing the quartz crystal tuningfork resonator in the case and mounting the quartz crystal tuning forkresonator on a mounting portion of the case, forming a metal film oneach of the first and second main surfaces of the first and secondquartz crystal tuning fork tines of the quartz crystal tuning forkresonator by an evaporation method so that a frequency of oscillation ofthe quartz crystal tuning fork resonator is in the range of 32.764 kHzto 32.772 kHz, and connecting the lid to the case to cover the open endthereof.
 4. A method according to claim 3; further comprising the stepof providing a surface mounting-type quartz crystal unit having thequartz crystal tuning fork resonator, the case and the lid.
 5. A methodaccording to claim 3; further comprising the steps of providing atubular-type quartz crystal unit having the quartz crystal tuning forkresonator, the case having two lead wires, and the lid, and mounting thequartz crystal tuning fork resonator on the two lead wires of the case.6. A method according to claim 3; wherein the series resistance R₁ ofthe fundamental mode of vibration of the quartz crystal tuning forkresonator is less than the series resistance R₂ of the second overtonemode of vibration thereof; and wherein the capacitance ratio r₁ of thefundamental mode of vibration of the quartz crystal tuning forkresonator is less than the capacitance ratio r₂ of the second overtonemode of vibration thereof.
 7. A method according to claim 6; wherein theforming step further comprises the step of forming each of the first andsecond quartz crystal tuning fork tines with a first side surface and asecond side surface opposite the first side surface; and furthercomprising the steps of forming a plurality of first electrodes on thefirst and second main surfaces of the first and second quartz crystaltuning fork tines and a plurality of second electrodes on the first andsecond side surfaces of the first and second quartz crystal tuning forktines, the first electrodes formed on the first and second main surfacesof the first quartz crystal tuning fork tine having an electricalpolarity opposite to an electrical polarity of the first electrodesformed on the first and second main surfaces of the second quartzcrystal tuning fork tine.
 8. A method according to claim 7; furthercomprising the steps of connecting the first electrodes formed on thefirst and second main surfaces of the first quartz crystal tuning forktines to the second electrodes formed on the first and second sidesurfaces of the second quartz crystal tuning fork tine so that the firstelectrodes of the first quartz crystal tuning fork tine and the secondelectrodes of the second quartz crystal tuning fork tine define a firstelectrode terminal 4 and connecting the second electrodes formed on thefirst and second side surfaces of the first quartz crystal tuning forktine to the first electrodes formed on the first and second mainsurfaces of the second quartz crystal tuning fork tine so that thesecond electrodes of the first quartz crystal tuning fork tine and thefirst electrodes of the second quartz crystal tuning fork tine define asecond electrode terminal.
 9. A method according to claim 8; wherein themerit value M₂ for the second overtone mode of vibration of the quartzcrystal tuning fork resonator is less than 30 so that the secondovertone mode of vibration thereof is suppressed.
 10. A method accordingto claim 6; wherein a ratio of an amplification rate α1 of thefundamental mode of vibration and an amplification rate α2 of the secondovertone mode of vibration of the amplification circuit is greater thanthat of a feedback rate β2 of the second overtone mode of vibration anda feedback rate β1 of the fundamental mode of vibration of the feedbackcircuit, a product of the amplification rate α1 and the feedback rate β1of the fundamental mode of vibration being greater than 1; and wherein astable factor S₁ of the fundamental mode of vibration of the quartzcrystal tuning fork resonator and a stable factor S₂ of the secondovertone mode of vibration thereof are defined by r₁/2Q₁ ² and r₂/2Q₂ ²,respectively, where S₁ is less than S₂.
 11. A method according to claim2; wherein the forming step includes the step of etching a quartzcrystal wafer to form the quartz crystal tuning fork base and the firstand second quartz crystal tuning fork tines; and further comprising thesteps of adjusting in a plurality of different steps a frequency ofoscillation of the quartz crystal tuning fork resonator, providing acase having a mounting portion therein and an open end, providing a lidfor covering the open end of the case, mounting the quartz crystaltuning fork resonator on the mounting portion of the case, andconnecting the lid to the case to cover the open end thereof.
 12. Amethod according to claim 11; wherein each of the first and secondquartz crystal tuning fork tines has a first side surface and a secondside surface opposite the first side surface; and wherein the formingstep comprises the step of disposing electrodes on the first and secondside surfaces of the first and second quartz crystal tuning fork tinesso that the electrodes disposed on the first and second side surfaces ofthe first quartz crystal tuning fork tine have an electrical polarityopposite to an electrical polarity of the electrodes disposed on thefirst and second side surfaces of the second quartz crystal tuning forktine.
 13. A method according to claim 11; wherein the forming stepincludes the steps of forming the quartz crystal tuning fork resonatorhaving a frequency of oscillation higher than 32.768 kHz and disposing ametal film on each of at least two of the first and second main surfacesof the first and second quartz crystal tuning fork tines of the quartzcrystal tuning fork resonator by a spattering method or an evaporationmethod so that the frequency of oscillation is in the range of 29.4 kHzto 32.75 kHz; and wherein the adjusting step comprises the steps ofadjusting the frequency of oscillation to a first preselected frequencyof oscillation and adjusting the frequency of oscillation to a secondpreselected frequency of oscillation by trimming the metal film on eachof at least two of the first and second main surfaces of the first andsecond quartz crystal tuning fork tines of the quartz crystal tuningfork resonator.
 14. A method according to claim 13; wherein the firstpreselected frequency of oscillation is in the range of 32.2 kHz to33.08 kHz; and wherein the second preselected frequency of oscillationis in the range of 32.764 kHz to 32.772 kHz.
 15. A method according toclaim 11; wherein the forming step further comprises the step of formingat least one groove having a plurality of stepped portions in at leastone of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines.
 16. A method according to claim15; wherein the step of forming at least one groove having a pluralityof stepped portions in at least one of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines comprises the step of forming a groove having a plurality ofstepped portions in each of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines so that a widthof at least one of the grooves formed in the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines is greater than a distance in the width direction of the at leastone groove measured from an outer edge of the at least one groove to anouter edge of the corresponding one of the first and second quartzcrystal tuning fork tines.
 17. A method according to claim 15; whereinthe step of forming the at least one groove in at least one of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines comprises the step of forming the at least one groovein each of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines, a width of the at least onegroove being defined by W₂, a distance in the width direction of the atleast one groove measured from a first outer edge of the at least onegroove to a first outer edge of the corresponding one of the first andsecond quartz crystal tuning fork tines being defined by W₁, and adistance in the width direction of the at least one groove measured froma second outer edge opposite to the first outer edge of the at least onegroove to a second outer edge opposite to the first outer edge of thecorresponding one of the first and second quartz crystal tuning forktines being defined by W₃; and wherein W₁ is greater than or equal toW₃.
 18. A method according to claim 15; wherein the step of forming theat least one groove in at least one of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines comprises the step of forming the at least one groove in each ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines, a width of the at least one groovebeing defined by W₂, a distance in the width direction of the at leastone groove measured from a first outer edge of the at least one grooveto a first outer edge of the corresponding one of the first and secondquartz crystal tuning fork tines being defined by W₁, and a distance inthe width direction of the at least one groove measured from a secondouter edge opposite to the first outer edge of the at least one grooveto a second outer edge opposite to the first outer edge of thecorresponding one of the first and second quartz crystal tuning forktines being defined by W₃; and wherein W1 is less than W₃.
 19. A methodaccording to claim 15; wherein the step of forming the at least onegroove in at least one of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines comprises the stepof forming the at least one groove in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines, each of the grooves having a first outer edge and a second outeredge opposite to the first outer edge in the width direction of thecorresponding one of the first and second quartz crystal tuning forktines; wherein each of the first and second quartz crystal tuning forktines has a first outer edge and a second outer edge opposite to thefirst outer edge; wherein a first part of each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines is formed between the first outer edge of the corresponding atleast one groove and the first outer edge of the corresponding one ofthe first and second quartz crystal tuning fork tines; wherein a secondpart of each of the first and second main surfaces of each of the firstand second quartz crystal tuning fork tines is formed between the secondouter edge of the corresponding at least one groove and the second outeredge of the corresponding one of the first and second quartz crystaltuning fork tines; and wherein an insulation material is disposed oneach of the first and second parts of the first and second main surfacesof each of the first and second quartz crystal tuning fork tines.
 20. Amethod according to claim 19; wherein the quartz crystal tuning forkbase has a first side surface connected to the first and second tuningfork tines, a second side surface opposite the first side surface, athird side surface having a cut portion, and a fourth side surfaceopposite the third side surface and having a cut portion, a width W₅ ofthe quartz crystal tuning fork base being disposed between the firstside surface and each of at least two of the cut portions of the thirdand fourth side surfaces, and a width W₆ of the quartz crystal tuningfork base being disposed between the second side surface and each of atleast two of the cut portions of the third and fourth side surfaces; andwherein W₅ is less than or equal to W₆.
 21. A method according to claim15; wherein the step of forming the at least one groove in at least oneof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines comprises the step of forming the atleast one groove in each of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines; and wherein aspaced-apart distance between the first and second quartz crystal tuningfork tines is greater than or equal to a width of the at least onegroove.
 22. A method according to claim 21; wherein each of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines has a central linear portion; wherein at least onegroove is formed in the central linear portion of each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines so that a width of at least one of the grooves formedin the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines is greater than or equal to a distancein the width direction of the at least one groove measured from an outeredge of the at least one groove to an outer edge of the correspondingone of the first and second quartz crystal tuning fork tines; andwherein a length of at least one of the grooves formed in the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines is within a range of 40% to 80% of a length of each ofthe first and second quartz crystal tuning fork tines.
 23. A methodaccording to claim 15; wherein the step of forming the at least onegroove in at least one of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines comprises the stepof forming a plurality of grooves having a plurality of stepped portionsin at least one of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines, each of the groovesbeing divided in a lengthwise direction of each of the first and secondquartz crystal tuning fork tines; wherein the forming step furthercomprises the steps of forming first electrodes on side surfaces of thefirst and second quartz crystal tuning fork tines and forming secondelectrodes having an electrical polarity opposite to an electricalpolarity of the first electrodes on each of at least four of the steppedportions of at least two of the grooves in at least one of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines; wherein a ratio W₂/W is greater than 0.35 and lessthan 1, where W₂ r represents a width of each of at least two of thegrooves in at least one of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines, and W representsa width of each of the first and second quartz crystal tuning forktines; wherein a ratio t₁/t is less than 0.79, where t₁ represents athickness of a base portion of each of at least two of the grooves and tis a thickness of each of the first and second quartz crystal tuningfork tines; and wherein an overall length of at least two of the grooveshaving the second electrodes is within a range of 40% to 80% of a lengthof each of the first and second quartz crystal tuning fork tines.
 24. Amethod according to claim 15; wherein a base portion of the at least onegroove in at least one of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines has a thickness t₁and a ratio t₁/t is less than 0.79, where t is a thickness of each ofthe first and second quartz crystal tuning fork tines; and wherein thethickness t₁ is zero to define a through-hole.
 25. A method according toclaim 11; wherein the forming step includes the steps of etching aquartz crystal wafer to form the quartz crystal tuning fork base and thefirst and second quartz crystal tuning fork tines so that the frequencyof oscillation of the quartz crystal tuning fork resonator is higherthan 32.768 kHz, and forming a metal film on each of at least two of thefirst and second main surfaces of the first and second quartz crystaltuning fork tines of the quartz crystal tuning fork resonator by aspattering method or an evaporation method so that the frequency ofoscillation is in the range of 29.4 kHz to 32.75 kHz; and wherein theadjusting step comprises the steps of adjusting in the quartz crystalwafer the frequency of oscillation of the quartz crystal tuning forkresonator by trimming the metal films on at least two of the first andsecond main surfaces of the first and second quartz crystal tuning forktines so that the frequency of oscillation is in the range of 32.2 kHzto 33.08 kHz and adjusting the frequency of oscillation thereof afterthe mounting step or after the mounting and connecting steps so that thefrequency of oscillation is in the range of 32.764 kHz to 32.772 kHz.26. A method according to claim 2; wherein the forming step includes thesteps of forming the quartz crystal tuning fork resonator having afrequency of oscillation higher than 32.768 kHz, and forming a metalfilm on each of at least two of the first and second main surfaces ofthe first and second quartz crystal tuning fork tines of the quartzcrystal tuning fork resonator by a spattering method or an evaporationmethod so that the frequency of oscillation is in the range of 29.4 kHzto 32.75 kHz; and further comprising the steps of providing a casehaving an open end, providing a lid for covering the open end of thecase, mounting the quartz crystal tuning fork resonator on a mountingportion within the case, adjusting the frequency of oscillation of thequartz crystal tuning fork resonator by trimming the metal film formedon each of at least two of the first and second main surfaces of thefirst and second quartz crystal tuning fork tines so that the frequencyof oscillation is in the range of 32.764 kHz to 32.772 kHz, andconnecting the lid to the case to cover the open end thereof.
 27. Amethod according to claim 26; wherein the series resistance R₁ of thefundamental mode of vibration of the quartz crystal tuning forkresonator is less than the series resistance R₂ of the second overtonemode of vibration thereof; wherein the capacitance ratio r₁ of thefundamental mode of vibration of the quartz crystal tuning forkresonator is less than the capacitance ratio r₂ of the second overtonemode of vibration thereof; and wherein a ratio of an amplification rateα1 of the fundamental mode of vibration and an amplification rate α2 ofthe second overtone mode of vibration of the amplification circuit isgreater than that of a feedback rate β₂ of the second overtone mode ofvibration and a feedback rate β₁ of the fundamental mode of vibration ofthe feedback circuit, a product of the amplification rate α₁ and thefeedback rate β₁ of the fundamental mode of vibration being greaterthan
 1. 28. A method according to claim 27; further comprising the stepof providing a surface mounting-type quartz crystal unit having thequartz crystal tuning fork resonator, the case and the lid.
 29. A methodaccording to claim 27; wherein the case has two lead wires; and whereinthe mounting step comprises the step of mounting the quartz crystaltuning fork resonator on the two lead wires of the case; and furthercomprising the step of providing a tubular-type quartz crystal unithaving the quartz crystal tuning fork resonator, the case and the lid.30. A method according to claim 27; wherein a ratio |−RL₁|/R₁ is greaterthan 2|−RL₂|/R₂−1, where |−RL₁| represents an absolute value of negativeresistance of the fundamental mode of vibration of the amplificationcircuit and |RL₂| represents an absolute value of negative resistance ofthe second overtone mode of vibration of the amplification circuit; andwherein the merit value M₂ for the second overtone mode of vibration ofthe quartz crystal tuning fork resonator is less than 30 so that thesecond overtone mode of vibration thereof is suppressed.
 31. A methodaccording to claim 27; wherein the step of providing an amplificationcircuit further comprises the step of providing an amplification circuithaving a feedback resistor; wherein the step of providing a feedbackcircuit further comprises the step of providing a feedback circuithaving a drain resistor and a contour mode quartz crystal resonatorformed by at least one of a particle method and a chemical etchingmethod to provide a vibrational portion, connecting portions located atends of the vibrational portion, supporting portions connected to thevibrational portion through the connecting portions, and electrodesdisposed opposite each other on upper and lower surfaces of thevibrational portion so that the electrodes have an opposite electricalpolarity, the contour mode quartz crystal resonator being one of awidth-extensional mode quartz crystal resonator, a length-extensionalmode quartz crystal resonator, and a Lame mode quartz crystal resonator;and further comprising the step of electrically connecting the contourmode quartz crystal resonator to the amplification circuit and to thecapacitors and the drain resistor of the feedback circuit.
 32. A methodaccording to claim 27; wherein the forming step includes the step offorming the quartz crystal tuning fork resonator in a quartz crystalwafer; and further comprising the steps of conducting a damageinspection of the quartz crystal tuning fork resonator in the quartzcrystal wafer and removing the quartz crystal tuning fork resonator fromthe quartz crystal wafer if it is determined from the damage inspectionthat the quartz crystal tuning fork resonator is damaged.
 33. A methodfor manufacturing a quartz crystal oscillator, comprising the steps of:forming by at least one of a chemical etching method, a physical etchingmethod and a mechanical method a quartz crystal tuning fork resonatorhaving a quartz crystal tuning fork base, first and second quartzcrystal tuning fork tines each connected to the quartz crystal tuningfork base and having a first main surface and a second main surfaceopposite the first main surface, and a plurality, of first electrodesdisposed on respective first and second main surfaces of the first andsecond quartz crystal tuning fork tines, the first electrodes disposedon the first and second main surfaces of the first quartz crystal tuningfork tine being connected together so that the first electrodes of thefirst quartz crystal tuning fork tine have a first electrical polarity,and the first electrodes disposed on the first and second main surfacesof the second quartz crystal tuning fork tine being connected togetherso that the first electrodes of the second quartz crystal tuning forktine have a second electrical polarity opposite to the first electricalpolarity, the quartz crystal tuning fork resonator having a fundamentalmode of vibration and a second overtone mode of vibration each comprisedof a flexural mode of an inverse phase, a series resistance R₁ of thefundamental mode of vibration, and a series resistance R₂ of the secondovertone mode of vibration; providing an amplification circuit having atleast an amplifier, a negative resistance −RL₁ of a fundamental mode ofvibration thereof, and a negative resistance −RL₂ of a second overtonemode of vibration thereof; providing a feedback circuit having thequartz crystal tuning fork resonator and a plurality of capacitors; andelectrically connecting together the amplifier of the amplificationcircuit and the quartz crystal tuning fork resonator and capacitors ofthe feedback circuit; wherein a ratio of an absolute value of thenegative resistance −RL₁ of the fundamental mode of vibration of theamplification circuit and the series resistance R₁ of the fundamentalmode of vibration of the quartz crystal tuning fork resonator is greaterthan that of an absolute value of the negative resistance −RL₂ of thesecond overtone mode of vibration of the amplification circuit and theseries resistance R₂ of the second overtone mode of vibration of thequartz crystal tuning fork resonator; and wherein a merit value M₁ ofthe fundamental mode of vibration of the quartz crystal tuning forkresonator is greater than a merit value M₂ of the second overtone modeof vibration thereof so that the second overtone mode of vibration ofthe quartz crystal tuning fork resonator is suppressed and a highfrequency stability is obtained for the fundamental mode of vibration ofthe quartz crystal tuning fork resonator, the merit values M₁ and M₂being defined by the ratios Q₁/r₁ and Q₂/r₂, respectively, where Q₁ andQ₂ represent a quality factor of the fundamental mode of vibration andthe second overtone mode of vibration, respectively, of the quartzcrystal tuning fork resonator and r₁ and r₂ represent a capacitanceratio of the fundamental mode of vibration and the second overtone modeof vibration, respectively, of the quartz crystal tuning fork resonator.34. A method according to claim 33; wherein the amplification circuithas a CMOS inverter and the feedback circuit has the capacitors and adrain resistor; and wherein the electrically connecting step comprisesthe step of electrically connecting the quartz crystal tuning forkresonator to the CMOS inverter of the amplification circuit and to thecapacitors and the drain resistor of the feedback circuit.
 35. A methodaccording to claim 34; wherein the forming step includes the step ofetching a quartz crystal wafer to form the quartz crystal tuning forkbase and the first and second quartz crystal tuning fork tines; andfurther comprising the steps of adjusting in a plurality of differentsteps a frequency of oscillation of the quartz crystal tuning forkresonator, providing a case having a mounting portion therein and anopen end, providing a lid for covering the open end of the case,mounting the quartz crystal tuning fork resonator on the mountingportion of the case, and connecting the lid to the case to cover theopen end thereof.
 36. A method according to claim 35; wherein theforming step includes the steps of forming the quartz crystal tuningfork resonator having a frequency of oscillation higher than 32.768 kHzand disposing a metal film on each of at least two of the first andsecond main surfaces of the first and second quartz crystal tuning forktines of the quartz crystal tuning fork resonator by a spattering methodor an evaporation method so that the frequency of oscillation is in therange of 29.4 kHz to 32.75 kHz; and wherein the adjusting step comprisesthe steps of adjusting the frequency of oscillation to a firstpreselected frequency of oscillation and adjusting the frequency ofoscillation to a second preselected frequency of oscillation by trimmingthe metal film on each of at least two of the first and second mainsurfaces of the first and second quartz crystal tuning fork tines of thequartz crystal tuning fork resonator.
 37. A method according to claim36; wherein the first preselected frequency of oscillation is in therange of 32.2 kHz to 33.08 kHz; and wherein the second preselectedfrequency of oscillation is in the range of 32.764 kHz to 32.772 kHz.38. A method for manufacturing a quartz crystal oscillator, comprisingthe steps of: forming by at least one of a chemical etching method, aphysical etching method and a mechanical method a quartz crystal tuningfork resonator having a quartz crystal tuning fork base, first andsecond quartz crystal tuning fork tines each connected to the quartzcrystal tuning fork base and having a first main surface and a secondmain surface opposite the first main surface, and at least one groovehaving a plurality of stepped portions formed in each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines, a spaced-apart distance between the first and secondquartz crystal tuning fork tines being within a range of 0.05 mm and0.35 mm and greater than or equal to the width of at least one of thegrooves in the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines, the quartz crystal tuning forkresonator having a fundamental mode of vibration and a second overtonemode of vibration each comprised of a flexural mode of an inverse phase,a series resistance R₁ of the fundamental mode of vibration, and aseries resistance R₂ of the second overtone mode of vibration; providingan amplification circuit having at least an amplifier, a negativeresistance −RL₁ of a fundamental mode of vibration thereof, and anegative resistance −RL₂ of a second overtone mode of vibration thereof;providing a feedback circuit having the quartz crystal tuning forkresonator and a plurality of capacitors; and electrically connectingtogether the amplifier of the amplification circuit and the quartzcrystal tuning fork resonator and capacitors of the feedback circuit;wherein a ratio of an absolute value of the negative resistance −RL₁ ofthe fundamental mode of vibration of the amplification circuit and theseries resistance R₁ of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is greater than that of an absolute valueof the negative resistance −RL₂ of the second overtone mode of vibrationof the amplification circuit and the series resistance R₂ of the secondovertone mode of vibration of the quartz crystal tuning fork resonator;and wherein a merit value M₁ of the fundamental mode of vibration of thequartz crystal tuning fork resonator is greater than a merit value M₂ ofthe second overtone mode of vibration thereof so that the secondovertone mode of vibration of the quartz crystal tuning fork resonatoris suppressed and a high frequency stability is obtained for thefundamental mode of vibration of the quartz crystal tuning forkresonator, the merit values M₁ and M₂ being defined by the ratios Q₁/r₁and Q₂/r₂, respectively, where Q₁ and Q₂ represent a quality factor ofthe fundamental mode of vibration and the second overtone mode ofvibration, respectively, of the quartz crystal tuning fork resonator andr₁ and r₂ represent a capacitance ratio of the fundamental mode ofvibration and the second overtone mode of vibration, respectively, ofthe quartz crystal tuning fork resonator.
 39. A method according toclaim 38; wherein the amplification circuit has a CMOS inverter and thefeedback circuit has the capacitors and a drain resistor; and whereinthe electrically connecting step comprises the step of electricallyconnecting the quartz crystal tuning fork resonator to the CMOS inverterof the amplification circuit and to the capacitors and the drainresistor of the feedback circuit.
 40. A method according to claim 39;wherein the forming step includes the step of etching a quartz crystalwafer to form the quartz crystal tuning fork base and the first andsecond quartz crystal tuning fork tines; and further comprising thesteps of adjusting in a plurality of different steps a frequency ofoscillation of the quartz crystal tuning fork resonator, providing acase having a mounting portion therein and an open end, providing a lidfor covering the open end of the case, mounting the quartz crystaltuning fork resonator on the mounting portion of the case, andconnecting the lid to the case to cover the open end thereof.
 41. Amethod according to claim 40; wherein the forming step further comprisesthe step of forming at least one groove having a plurality of steppedportions in at least one of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines.
 42. A methodaccording to claim 38; wherein the forming step comprises the step offorming the first and second quartz crystal tuning fork tines in a stepdifferent from and before a step of forming the at least one groove. 43.A method according to claim 42; wherein the at least one groove has awidth within a range of 0.02 mm to 0.068 mm.
 44. A method according toclaim 38; wherein the forming step comprises the step of forming thefirst and second quartz crystal tuning fork tines in a step differentfrom and after a step of forming the at least one groove.
 45. A methodaccording to claim 38; wherein a ratio W₂/W is greater than 0.35 andless than 1, where W₂ represents a width of the at least one grooveformed in the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines and W represents a width of eachof the quartz crystal tuning fork tines; wherein the forming stepfurther comprises the steps of disposing a first electrode on each of atleast two of side surfaces of one of the first and second tuning forktines and disposing a second electrode having an electrical polaritydifferent from that of the first electrode on each of at least two ofthe stepped portions of the groove formed in each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines; and wherein a length of at least one of the grooveshaving the stepped portion on which the second electrode is disposed iswithin a range of 40% to 80% of a length of each of the first and secondquartz crystal tuning fork tines.
 46. A method according to claim 45;wherein the series resistance R₁ of the fundamental mode of vibration ofthe quartz crystal tuning fork resonator is less than the seriesresistance R₂ of the second overtone mode of vibration thereof; andwherein the capacitance ratio r₁ of the fundamental mode of vibration ofthe quartz crystal tuning fork resonator is less than the capacitanceratio r₂ of the second overtone mode of vibration thereof.
 47. A methodaccording to claim 45; wherein the merit value M₂ for the secondovertone mode of vibration of the quartz crystal tuning fork resonatoris less than 30 so that the second overtone mode of vibration thereof issuppressed; and wherein a stable factor S₁ of the fundamental mode ofvibration of the quartz crystal tuning fork resonator and a stablefactor S₂ of the second overtone mode of vibration thereof are definedby r₁/2Q₁ ² and r₂/2Q₂ ², respectively, where S₁ is less than S₂.
 48. Amethod according to claim 45; further comprising the step of providing aquartz crystal unit by disposing the quartz crystal tuning forkresonator in an interior space of a case having an opening and coveringthe opening of the case with a lid; and further comprising the step ofdisposing at least one of a metal and a glass into a through-hole formedin one of the case and the lid to maintain the interior space of case ofthe quartz crystal unit in a vacuum.
 49. A method according to claim 45;wherein the capacitors of the feedback circuit comprise a gate sidecapacitor having a capacitance C_(g) and a drain side capacitor having acapacitance C_(d); and wherein a load capacitance C_(L) is less than 18pF, where C_(L) is defined by C_(g)C_(d)/(C_(g)+C_(d)).
 50. A methodaccording to clam 38; wherein the forming step includes the step offorming the first and second quartz crystal tuning fork tinessimultaneously with the corresponding grooves.
 51. A method formanufacturing a quartz crystal oscillator, comprising the steps of:forming by at least one of a chemical etching method, a physical etchingmethod, and a mechanical method a quartz crystal tuning fork resonatorhaving a quartz crystal tuning fork base and first and second quartzcrystal tuning fork tines each connected to the quartz crystal tuningfork base and having a first main surface and a second main surfaceopposite the first main surface, the quartz crystal tuning forkresonator having a fundamental mode of vibration and a second overtonemode of vibration each comprised of flexural mode of an inverse phase, aseries resistance R₁ of the fundamental mode of vibration and a seriesresistance R₂ of the second overtone mode of vibration; providing anamplification circuit having at least a CMOS inverter, a negativeresistance −RL₁ of a fundamental mode of vibration thereof, and anegative resistance −RL₂ of a second overtone mode of vibration thereof;providing a feedback circuit having at least the quartz crystal tuningfork resonator and a plurality of capacitors; and electricallyconnecting the quartz crystal tuning fork resonator to the CMOS inverterof the amplification circuit and to the capacitors of the feedbackcircuit; wherein a ratio |−RL₁|/R₁ is greater than 2|−RL₂|/R₂−1, where|−RL₁| represents an absolute value of the negative resistance of thefundamental mode of vibration of the amplification circuit and |−RL₂|represents an absolute value of the negative resistance of the secondovertone mode of vibration of the amplification circuit; and wherein amerit value M₁ of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is greater than a merit value M₂ of thesecond overtone mode of vibration thereof, the merit values M₁ and M₂being defined by the ratios Q₁/r₁ and Q₂/r₂ respectively, where Q₁ andQ₂ represent a quality factor of the fundamental mode of vibration andthe second overtone mode of vibration, respectively, of the quartzcrystal tuning fork resonator and r₁ and r₂ represent a capacitanceratio of the fundamental mode of vibration and the second overtone modeof vibration, respectively, of the quartz crystal tuning fork resonator.52. A method according to claim 51; wherein the forming step furthercomprises the step of forming at least one groove having a plurality ofstepped portions in each of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines.
 53. A methodaccording to claim 52; wherein a spaced-apart distance between the firstand second quartz crystal tuning fork tines is within a range of 0.05 mmto 0.35 mm and is greater than or equal to a width of at least one ofthe grooves in the first and second main surfaces of each of the firstand second quartz crystal tuning fork tines; and wherein the formingstep comprises the step of forming the first and second quartz crystaltuning fork tines in a step different from and before a step of formingthe at least one groove.
 54. A method according to claim 53; whereineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines has a central linear portion;wherein at least one groove is formed in the central linear portion ofeach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that a width of at least oneof the grooves formed in the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines is greater than adistance in the width direction of the at least one groove measured froman outer edge of the at least one groove to an outer edge of thecorresponding one of the first and second quartz crystal tuning forktines; and wherein a length of at least one of the grooves formed in thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines is within a range of 40% to 80% of a length ofeach of the first and second quartz crystal tuning fork tines.
 55. Amethod according to claim 52; wherein a spaced-apart distance betweenthe first and second quartz crystal tuning fork tines is within a rangeof 0.05 mm to 0.35 mm and is greater than or equal to a width of atleast one of the grooves in the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines; and whereinthe forming step comprises the step of forming the first and secondquartz crystal tuning fork tines in a step different from and after astep of forming the at least one groove.
 56. A method according to claim55; wherein each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines has a central linearportion; wherein at least one groove is formed in the central linearportion of each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines so that a width of atleast one of the grooves formed in the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines is graterthan a distance in the width direction of the at least one groovemeasured from an outer edge of the at least one groove to an outer edgeof the corresponding one of the first and second quartz crystal tuningfork tines; and wherein a length of at least one of the grooves formedin the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines is within a range of 40% to 80% of alength of each of the first and second quartz crystal tuning fork tines.57. A method according to claim 52; wherein a spaced-apart distancebetween the first and second quartz crystal tuning fork tines is withina range of 0.05 mm to 0.35 mm and is greater than or equal to a width ofat least one of the grooves in the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines; andwherein the forming step includes the step of forming the first andsecond quartz crystal tuning fork tines simultaneously with thecorresponding grooves.
 58. A method according to claim 57; wherein eachof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines has a central linear portion; whereinat least one groove is formed in the central linear portion of each ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines so that a width of at least one of thegrooves formed in the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines is greater than orequal to a distance in the width direction of the at least one groovemeasured from an outer edge of the at least one groove to an outer edgeof the corresponding one of the first and second quartz crystal tuningfork tines; and wherein a length of at least one of the grooves formedin the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines; and wherein a length of at least oneof the grooves formed in the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines is within a rangeof 40% to 80% of a length of each of the first and second quartz crystaltuning fork tines.